We define the spatial search space using the previously localized eyes and
mouth. This will restrict the signature analysis so that no facial contours or
external edges will affect edge signature analysis. Figure
shows the region where signature analysis will be performed. The edges
contained by this triangle are summed into bins corresponding to their yvalue. These bins form the vertical signature of the nose. The bin with the
strongest edge content is the one that corresponds to the vertical position of
the nose's bottom. Figure also shows the projected
gradient map and the signature that was computed in the search space. The
nose's bottom position corresponds to the peak value of the signature.

However, we are interested in the nose tip, not the nose bottom. The nose tip
characterizes 3D pose more clearly since it strongly protrudes from the
ellipsoidal structure of the head. Assume the nose bottom was detected at
position
noseBottomy at the peak signature value of
noseBottomvalue.
We search a window of height of up to
above the nose bottom
for a weaker signature value. The nose tip is defined as the closest point in
the window with a signature value below
.
This
simple adjustment is depicted in Figure . The positions
of the nose bottom and the nose tip are shown as horizontal lines in
Figure . Note the effect of this computation is quite minor
and the nose-tip is only 2 pixels above the nose-bottom. Although the
definition of the nose-tip and the use of the 40% threshold are somewhat
arbitrary, we merely wish to move out of the region corresponding to the nose
bottom (nostrils and shading) by a marginal amount so that the position
detected has a 3D height. In other words, we wish to move upwards a small
distance so that we localize a point somewhere on the nose, taking advantage
of its 3D protrusion on the face (which specifies pose more exactly than
non-protruding features on the face). Furthermore, the small upwards
adjustment from nose-bottom to nose-tip does not have to be exact as long as
we are somewhere on the nose and not on the junction between the nose-bottom and
the face (which is not a 3D protrusion). Usually, the nose tip is brighter
than the rest of the nose and the nose bottom is darker. However, the
transition from nose tip to nose bottom or bright to dark is somewhat gradual.
By moving upwards in search of a 40% signature value (rather than the
maximum), we are searching for the beginning of this transition and moving
closer to the true nose position in the process.

Figure 3.29:
Finding the nose tip from the nose bottom using the edge signature.

Figure 3.30:
The nose-bottom-line and the nose-tip-line.

Thus, we have roughly determined the height of the nose tip with respect to
the eyes. However, we are uncertain of the exact horizontal position of the
nose. The required localization is difficult to perform using simple signature
analysis. This is mainly due to the fact that noses have the same tone as the
rest of the skin-covered face and hence have low perceptual significance.
Thus, a more sensitive nose finding technique will be utilized to isolate the
horizontal position of the nose. This technique requires the introduction of
normalization and recognition algorithms which will be detailed in Chapter 4.
For now, the nose-localization module merely outputs a height value at the
nose-tip position so we do not have a single locus for the nose but, rather, a
line of possible loci for the nose. This nose-line lies between the two eyes
at a fixed perpendicular distance below them. Thus, the output of the nose
detection defines a nose-line (as opposed to a nose locus) along which the
nose is situated as depicted in Figure . The nose-line
crosses the nose tip and is parallel to the line formed by the two eyes.
Additionally, its length is equal to the intra-ocular distance. In other
words, the nose-line starts below the left eye and ends below the right eye.